Solving the mathematics of image formation with fast cameras

By Brooke Kuei

Modern electron microscopes are capable of forming images with resolutions less than 50 picometers – 340,000 times smaller than the width of a human hair – making it an important tool for studying materials at the atomic level. When the sample being studied is very thin (less than 50 angstroms), the images formed through the interaction between the electrons and the material are directly related to the material’s structure. In a thicker sample, however, electrons that travel through the material undergo so many interactions along the way that the resultant image can be difficult to interpret.

In a study recently published in Physical Review Letters, a team of Molecular Foundry staff and users from Monash University in Australia overcame this problem by using a fast readout electron camera to collect precise information on how electrons are deflected by the sample, allowing the researchers to solve the structure of a thick crystal.

“The mathematical equations that relate the images formed in the electron microscope to the structure that is being imaged are often complicated,” said Hamish Brown, post-doctoral researcher at the Foundry’s National Center for Electron Microscopy (NCEM) and lead author of the study. A general, direct method for solving an unknown structure from experimental data has been a mystery until this study, despite the underlying equations being known since the 1920s.

One previous approach for solving this problem assumed a given structure and predicted what image would be produced by simulating the way an electron might move through this structure. Another method took the opposite approach – solving for the structure based on simplified, approximate equations describing how electrons travel through materials. This second strategy has been limited to thin samples where the interactions between the electrons and the sample are relatively simple.

In this work, the researchers were able to generalize the latter approach on a thick sample with the help of a fast electron detector, or camera, that is able to record images faster than 100 frames per second. Using this camera, the researchers were able to scan a tiny electron beam (about the width of an atom) across their sample, recording the angles to which electrons are deflected at each location in the sample. They repeated this multiple times while changing the focus of the beam.